Emergence of collective behavior in a system of autonomous agents

We study the properties of emergent collective behavior in a system of interacting autonomous agents. The system evolves in time according to two rules of communication, one from interactions between agents and another one from interactions of the agents with an additional agent which evolves in time in a periodic and stable manner. The application of these two rules is decided by a prescribed probability distribution. We analyze the emergence and the efficiency (coordination) with which collective patterns are constructed in time as a function of the parameters of the system

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

Resonances of the cusp family

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius--Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.

One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure

User generated spatial content: an analysis of the phenomenon and its challenges for mapping agencies

Since the World Wide Web (Web) became a medium to serve information, its impact on geographic information has been constantly growing. Today the evolution of the bi-directional Web 2.0 has created the phenomenon of User Generated Spatial Content. In this Thesis the focus is into analysing different aspects of this phenomenon from the perspective of a mapping agency and also developing methodologies for meeting the challenges revealed. In this context two empirical studies are conducted. The first examines the spatial dimension of the popular Web 2.0 photo-sharing websites like Flickr, Panoramio, Picasa Web and Geograph, mainly investigating whether such Web applications can serve as sources of spatial content. The findings show that only Web applications that urge users to interact directly with spatial entities can serve as universal sources of spatial content. The second study looks into data quality issues of the OpenStreetMap, a popular wiki-based Web mapping application. Here the focus is on the positional accuracy and attribution quality of the user generated spatial entities. The research reveals that positional accuracy is fit for a number of purposes. On the other hand, the user contributed attributes suffer from inconsistencies. This is mainly due to the lack of a methodology that could help to the formalisation of the contribution process, and thus enhance the overall quality of the dataset. The Thesis explores a formalisation process through an XML Schema for remedying this problem. Finally, the advantages of using vector data in order to enhance interactivity and thus create more efficient and bi-directional Web 2.0 mapping applications is analysed and a new method for vector data transmission over the Web is presented